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Free CA Quantitative Aptitude Practice Questions & Answers
500 exam-style Quantitative Aptitude questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 481
In systematic sampling, units are selected:
Select an option first.
Correct answer: D — At regular intervals from the sampling frame after a random start
Explanation: Every kth unit is taken after a random starting point, which is simpler and faster than drawing each unit independently. The danger is a hidden PERIODICITY in the frame that coincides with the interval, which would produce a systematically unrepresentative sample.
Question 482
Fisher's index is described as ideal partly because it satisfies:
Select an option first.
Correct answer: B — Both the time reversal test and the factor reversal test
Explanation: The time reversal test requires that the index computed forwards multiplied by the index computed backwards equals 1; the factor reversal test requires that the price index multiplied by the quantity index equals the value index. Fisher's satisfies both, while Laspeyres' and Paasche's satisfy neither - it fails only the circular test.
Question 483
In a normal distribution, approximately 95% of the observations lie within how many standard deviations of the mean?
Select an option first.
Correct answer: B — 1.96
Explanation: The central 95% lies within 1.96 standard deviations either side of the mean, leaving 2.5% in each tail. The related values are 1.645 for 90% and 2.58 for 99%. These three multipliers recur throughout estimation and testing and are worth committing to memory as a set.
Question 484
The circular test is satisfied by:
Select an option first.
Correct answer: A — The simple geometric mean of price relatives and Kelly's fixed-weight aggregative index
Explanation: The circular test extends the time reversal test to three or more periods, requiring the chain of indices to return to unity. Neither Laspeyres, Paasche nor even Fisher satisfies it, because their weights change with the period. Only indices with FIXED weights - the simple geometric mean of price relatives and Kelly's index - pass it. This is the one test Fisher's ideal index fails.
Question 485
The time reversal test requires that:
Select an option first.
Correct answer: A — The index for the current year multiplied by the index for the base year, computed in reverse, equals unity
Explanation: Formally, P01 multiplied by P10 must equal 1 when the factor of 100 is removed - the index computed forwards and then backwards must return to the starting point. Distractor B states the FACTOR reversal test. Fisher's index satisfies both, which is a large part of why it is called ideal.
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Question 486
An ogive is used to determine:
Select an option first.
Correct answer: B — The median and the quartiles
Explanation: An ogive plots cumulative frequencies against class boundaries, so any positional value can be read from it - the median at half the total frequency, the quartiles at one quarter and three quarters, and percentiles likewise. Values requiring totals, such as the mean, cannot be read from a graph.
Question 487
The regression equation of y on x is y = 2 + 0.6x. If x increases by 5, y increases by:
Select an option first.
Correct answer: B — 3
Explanation: The coefficient 0.6 is the change in y for a UNIT change in x, so a rise of 5 in x raises y by 0.6 x 5 = 3. The intercept of 2 plays no part, because it is the same before and after and cancels in the difference. Distractor D mistakes the intercept for the slope.
Question 488
A value index is obtained by:
Select an option first.
Correct answer: C — Multiplying the price index by the quantity index and dividing by 100
Explanation: Value is price times quantity, so the value index combines the two in the same way, with the division by 100 correcting for both being expressed on a base of 100. The requirement that this identity hold exactly is the FACTOR reversal test, which Fisher's index satisfies.
Question 489
The variance of the first five natural numbers is:
Select an option first.
Correct answer: D — 2
Explanation: The mean of 1 to 5 is 3; the deviations are -2, -1, 0, 1 and 2, whose squares total 10; dividing by n = 5 gives a variance of 2. Distractor A divides by (n - 1), which gives the SAMPLE variance - at this level, unless the question says sample, divide by n. The standard deviation would be the square root of 2.
Question 490
If the standard deviation of a distribution is 5 and its mean is 25, the variance is:
Select an option first.
Correct answer: B — 25
Explanation: Variance is the square of the standard deviation, so it is 5 squared = 25. The mean is not needed at all - it is given only to tempt a coefficient of variation calculation, which would be 20%. Read precisely which measure is asked for; variance, standard deviation and coefficient of variation are three different answers from the same data.
Question 491
The variance of the values 2, 4, 6 and 8 is:
Select an option first.
Correct answer: A — 5
Explanation: The mean is 5; the deviations are -3, -1, 1 and 3, whose squares total 20; dividing by n = 4 gives a variance of 5. Distractor D is the sum of squares before dividing. The standard deviation would be the square root of 5, about 2.24.
Question 492
A student scores 80 in a paper carrying 3 credits and 60 in a paper carrying 2 credits. The weighted mean score is:
Select an option first.
Correct answer: B — 72
Explanation: Weighted mean = (80 x 3 + 60 x 2) / (3 + 2) = (240 + 120) / 5 = 72. Distractor A is the simple average, which would be correct only if the credits were equal. Because the higher score carries the greater weight, the weighted mean must lie ABOVE 70 - a direction check that removes two options at once.
Question 493
Weights are used in the construction of an index number in order to:
Select an option first.
Correct answer: B — Reflect the relative importance of the items included
Explanation: An unweighted index treats a change in the price of salt as equal in importance to the same proportional change in the price of housing, which no one would accept. Weights - usually quantities consumed or values spent - make each item count in proportion to its actual significance.
Question 494
Two values, 40 and 60, carry weights of 2 and 3 respectively. The weighted mean is:
Select an option first.
Correct answer: A — 52
Explanation: Weighted mean = (40 x 2 + 60 x 3)/(2 + 3) = (80 + 180)/5 = 52. Distractor B is the simple average, correct only if the weights were equal. Because the larger value carries the greater weight, the answer must exceed 50 - a check that removes two options.
Question 495
The Poisson distribution is appropriate where the probability of success is:
Select an option first.
Correct answer: B — Very small while the number of trials is very large
Explanation: The Poisson arises as the limit of the binomial when n tends to infinity and p tends to zero with np held finite - which is why it models rare events such as accidents per month or defects per batch. It needs only the mean, since its variance equals its mean, and n need never be known.
Question 496
Spearman's rank correlation is the appropriate measure when:
Select an option first.
Correct answer: D — The data are given as ranks, or are qualitative and can only be ranked
Explanation: Rank correlation needs only an ordering, so it serves for qualitative characteristics such as beauty, honesty or efficiency, which cannot be measured on a numerical scale. It is also useful where extreme values would distort Karl Pearson's coefficient, since ranks compress outliers.
Question 497
The mean of 5 observations is 20. When one observation is removed, the mean of the remaining 4 is 18. The observation removed was:
Select an option first.
Correct answer: A — 28
Explanation: The original total is 5 x 20 = 100 and the remaining total is 4 x 18 = 72, so the removed observation is 28. Because the mean FELL when it was removed, the value must have been above the original mean of 20 - a direction check that eliminates two options before any arithmetic.
Question 498
If the covariance between two variables is zero, the coefficient of correlation is:
Select an option first.
Correct answer: D — Zero
Explanation: The correlation coefficient is the covariance divided by the product of the two standard deviations, so a zero numerator makes it zero, provided neither standard deviation is zero. It follows that zero covariance means no LINEAR relationship - though a non-linear one may still exist.
Question 499
The standard deviation of the values 4, 4, 4 and 4 is:
Select an option first.
Correct answer: C
Explanation: All the values are identical, so every deviation from the mean is zero and the standard deviation is zero. This is the smallest value it can take - being the square root of a mean of squares, it can never be negative. Zero dispersion means the data are perfectly uniform.
Question 500
Skewness is zero for:
Select an option first.
Correct answer: B — A symmetrical distribution
Explanation: Skewness measures departure from symmetry, so it vanishes precisely when the two tails balance - at which point the mean, median and mode all coincide. Note that a mean of zero says nothing about symmetry, which is what distractor D tests: location and shape are independent properties.
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